Prior to the present invention, there has not existed a machine comparable to that of the present invention, there being no fully automatic machine which may be left to operate to both collect, stack, and align, and deliver the stacks to a take-off point beyond the stacking machine. In contrast, conventionally several workers have been necessary to attend the receiving of each of a series of sheets of cardboard produced and delivered on a conveyor, having to thereafter manually stack and manually align and manually transport the same before or after stacking to a suitable off-the-conveyor location, as well as the eventual transport to a shipping or storage location. More recently, a machine was devised which purported to simplify matters, by providing for automatic piling of the sheets one upon the other, but required/requires constant attendance and manual assistance of and by one or more workers to prevent excessive stacking and to align during and after the stacking to prevent hang-ups on the equipment. Thereafter, the stacks had to be manually moved to an out-of-the-way point.